Details

sample44.0ms

Algorithm

intervals

Results

19.0ms	92×	body	1280	valid
7.0ms	43×	body	640	valid
6.0ms	175×	body	80	valid
3.0ms	26×	body	320	valid
1.0ms	8×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	3
1	18	3
2	26	3
3	48	3
4	110	3
5	318	3
6	1623	3
7	5001	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
2.2b	(- (exp (* a x)) 1.0)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

1.0ms	(exp (* a x))
4.0ms	(- (exp (* a x)) 1.0)

series50.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(exp (* a x))
34.0ms	(- (exp (* a x)) 1.0)

simplify40.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	115	135
1	333	127
2	1116	125
3	5001	125

prune72.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.7b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.0b	(pow (- (exp (* a x)) 1.0) 3)
0.0b	(cbrt (pow (- (exp (* a x)) 1.0) 3))
2.2b	(- (exp (* a x)) 1.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`cbrt-prod`
10×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
8×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `exp-prod` `exp-to-pow` `pow-pow` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `rem-exp-log` `rem-cube-cbrt`

Counts

4 → 80

Calls

4 calls:

1.0ms	(exp (* a x))
6.0ms	(pow (- (exp (* a x)) 1.0) 3)
6.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
4.0ms	(- (exp (* a x)) 1.0)

series134.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(exp (* a x))
51.0ms	(pow (- (exp (* a x)) 1.0) 3)
33.0ms	(cbrt (pow (- (exp (* a x)) 1.0) 3))
37.0ms	(- (exp (* a x)) 1.0)

simplify38.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	269	550
1	1076	527
2	5001	516

prune166.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ (exp (* a x)) 1.0) 3)
0.0b	(cbrt (/ (pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
0.0b	(* (exp (* a x)) (exp (* a x)))
2.1b	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

202×	`cbrt-prod`
196×	`times-frac`
156×	`*-un-lft-identity`
116×	`unpow-prod-down` `cube-prod`
98×	`add-sqr-sqrt`
96×	`add-cube-cbrt`
30×	`distribute-lft-out`
29×	`cube-mult` `unpow3` `difference-of-squares` `sqr-pow`
18×	`add-log-exp`
12×	`pow1` `exp-prod` `exp-to-pow`
7×	`add-cbrt-cube`
5×	`add-exp-log` `pow-prod-down` `pow-sqr` `pow-prod-up`
4×	`cube-div`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`flip3-+` `associate-/r/` `flip-+`
1×	`pow2` `pow-to-exp` `sub-neg` `cbrt-div` `flip3--` `pow-pow` `pow-plus` `pow1/3` `diff-log` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 288

Calls

4 calls:

6.0ms	(pow (+ (exp (* a x)) 1.0) 3)
26.0ms	(cbrt (/ (pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
6.0ms	(* (exp (* a x)) (exp (* a x)))
6.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))

series168.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (+ (exp (* a x)) 1.0) 3)
64.0ms	(cbrt (/ (pow (- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
24.0ms	(* (exp (* a x)) (exp (* a x)))
45.0ms	(- (* (exp (* a x)) (exp (* a x))) (* 1.0 1.0))

simplify164.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	775	6124
1	4027	5982
2	5001	5918

prune561.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 7.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (/ (pow (- (exp (* a (+ x x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
0.0b	(pow (- (exp (* a (+ x x))) (* 1.0 1.0)) 3)
0.0b	(pow (+ (exp (* a x)) 1.0) 3)
2.1b	(- (exp (* a (+ x x))) (* 1.0 1.0))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

258×	`cbrt-prod`
252×	`times-frac`
183×	`*-un-lft-identity`
166×	`unpow-prod-down` `cube-prod`
138×	`add-sqr-sqrt`
107×	`add-cube-cbrt`
93×	`difference-of-squares`
62×	`exp-sum`
38×	`distribute-lft-out`
34×	`cube-mult` `unpow3` `sqr-pow`
31×	`distribute-rgt-in` `distribute-lft-in`
6×	`pow1` `add-exp-log` `cube-div` `pow-unpow` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `flip3--` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip--` `flip-+` `rem-cube-cbrt`
1×	`sub-neg` `cbrt-div` `pow1/3` `diff-log` `div-inv`

Counts

4 → 340

Calls

4 calls:

24.0ms	(cbrt (/ (pow (- (exp (* a (+ x x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
7.0ms	(pow (- (exp (* a (+ x x))) (* 1.0 1.0)) 3)
6.0ms	(pow (+ (exp (* a x)) 1.0) 3)
7.0ms	(- (exp (* a (+ x x))) (* 1.0 1.0))

series201.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(cbrt (/ (pow (- (exp (* a (+ x x))) (* 1.0 1.0)) 3) (pow (+ (exp (* a x)) 1.0) 3)))
58.0ms	(pow (- (exp (* a (+ x x))) (* 1.0 1.0)) 3)
30.0ms	(pow (+ (exp (* a x)) 1.0) 3)
49.0ms	(- (exp (* a (+ x x))) (* 1.0 1.0))

simplify172.0ms

Algorithm

egg-herbie

Counts

352 → 352

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	927	6726
1	4629	6548
2	5001	6412

prune411.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 7.6b

regimes202.0ms

Accuracy

89.7% (2.2b remaining)

Error of 10.2b against oracle of 8.0b and baseline of 29.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	35
1	53	35

end0.0ms

sample1.3s

Algorithm

intervals

Results

608.0ms	2746×	body	1280	valid
201.0ms	1339×	body	640	valid
194.0ms	5526×	body	80	valid
81.0ms	739×	body	320	valid
29.0ms	368×	body	160	valid